Method and apparatus for detecting and locating noise sources not correlated

ABSTRACT

According to the invention, the method of detecting and locating sources of noise each emitting respective signals S j  with j=1 to M, detection being performed using sensors each delivering a respective time-varying electrical signal s i  with i varying from 1 to N, consists in taking the time-varying electrical signals delivered by the sensors, each signal s i (t) delivered by a sensor being the sum of the signals S j  emitted by the noise sources, in amplifying and filtering the time-varying electrical signals as taken, in digitizing the electrical signals, in calculating the functional  
         f   ⁡     (       n   1     ,   …   ⁢           ,     n   j     ,   …   ⁢           ,     n   N       )       =       ∑     k   ≠   1               ⁢           ⁢     R   k1           
 
with coefficients R kl  being a function of the vectors n j  giving the directions of the noise sources, and in minimizing the functional f in such a manner as to determine the directions n j  of the noise sources.

FIELD OF THE INVENTION

The present invention relates to detecting and locating sources of noise in the general sense, using sensors that are appropriate for the nature of the noise source.

The invention relates to a method of detecting and locating noise sources disposed in a space of one, two, or three dimensions and optionally correlated with one another, and presenting emission spectra of narrow or broad band.

The invention finds particularly advantageous applications in the field of locating sources of noise optionally accompanied by echo and coming, for example, from vehicles, ships, aircraft, or firearms.

BACKGROUND OF THE INVENTION

In numerous applications, a need arises to be able to locate in relatively accurate manner a source of noise in order to take measures to neutralize it. Numerous solutions are known in the prior art for acoustically locating noise sources. The main known solutions make use of techniques for correlating signals delivered by detection sensors.

Those techniques present the drawback of being particularly sensitive to interfering noise occurring in the environment of the measurement sensors. Furthermore, it must be considered that those techniques constitute specific methods that are adapted to each application under consideration.

The technique in most widespread use involves antennas having a large number of sensors (several hundred) and a large computer system implementing beam forming so as to aim in a given direction in order to increase the signal-to-noise ratio. That method does not make any a priori assumption concerning the number of sources and any possible correlation between them, which leads to a loss of resolution.

OBJECTS AND SUMMARY OF THE INVENTION

There therefore exists a need to have a general method of detecting and locating noise sources in space, when the number of noise sources is small and is known or overestimated.

The invention seeks to satisfy this need by proposing a method of detecting and locating noise sources by means of sensors adapted to the nature of the noise source, the method presenting low implementation costs.

To achieve this object, the method of the invention consists:

-   -   in taking the time-varying electrical signals delivered by the         sensors (Y_(i)), each signal s_(i)(t) delivered by a sensor         being the sum of the signals S_(j) emitted by the noise sources         (X_(j));     -   in amplifying and filtering the time-varying electrical signals         as taken;     -   in digitizing the electrical signals;     -   in calculating the functional         ${f\left( {n_{1},\ldots\quad,n_{j},\ldots\quad,n_{N}} \right)} = {\sum\limits_{k \neq 1}^{\quad}\quad R_{k1}}$         with the coefficients R_(kl) being a function of the vectors         n_(j) giving the directions of the noise sources; and     -   in minimizing the functional in such a manner as to determine         the directions of the noise sources.

BRIEF DESCRIPTION OF THE DRAWINGS

Various other characteristics appear from the description given below with reference to the accompanying drawing which shows embodiments and implementations of the invention as non-limiting examples.

FIG. 1 is a diagram showing the principle of the detection method of the invention.

FIG. 2 is a diagram showing a detail characteristic to the method of the invention.

FIG. 3 is a diagram showing the method of locating two noise sources using two sensors.

MORE DETAILED DESCRIPTION

As can be seen in FIG. 1, the method of the invention consists in locating noise sources X_(l), X₂, . . . , X_(j), . . . , X_(M) where j varies over the range 1 to M, the sources being distributed in space and each emitting a respective signal S_(j) with j varying in the range 1 to M. The method of the invention consists in locating the noise sources X_(j) using sound wave or vibration sensors Y₁, Y₂, . . . , Y_(i), . . . , Y_(N) where i varies over the range 1 to N, each delivering a respective time-varying electrical signal s₁, s₂, . . . , s_(i), . . . , s_(N).

The method consists in taking the time-varying electrical signals s_(i)(t) delivered by each of the sensors and representative of the sums of the signals S_(j) emitted by the noise sources X_(j), The signals s_(i)(t) received on the N sensors on the basis of the sum of the contributions of the various sources is written as follows: ${s_{i}(t)} = {\sum\limits_{j = 1}^{M}\quad{A_{ij}{S_{j}\left( {t - \frac{r_{ij}}{c}} \right)}}}$ where i=1 to N, r_(ij) is the distance between the noise source X_(j) and the sensor Y_(i), and c is the speed of sound in the ambient medium.

The term A_(ij) represents the attenuation due to propagation together with the sensitivity factor of the sensors and is expressed as follows: A _(ij) =B _(i) C(r _(ij)) where i=1 to N and j=1 to M, where B_(i) is the sensitivity coefficient of sensor Y_(i) and where C(r_(ij)) is the attenuation coefficient due to propagation over a distance r_(ij).

The sensors Y_(i) are associated with respective electronic units (not shown) for amplifying and lowpass filtering the signals they pick up. The sensors are preferably matched in modulus and phase so that their sensitivities are identical. Thus, B_(i)=G for i=1 to N.

Advantageously, in order to facilitate implementing the antenna of sensors as defined above, the sensors Y_(i) are placed relatively close to one another. Consequently, for remote sources, the distance r_(ij) is of the order of the distance r_(j), i.e. the distance between the center of gravity of the sensors and the source X_(j). Thus, attenuation becomes a function of the distance r_(j) only with C(r_(ij))=C(r_(j)), with i=1 to N and j=1 to M.

It can be deduced therefrom that: A _(ij) =G·C(r _(j))=a(r _(j)) where i=1 to N and j=1 to M and: ${s_{i}(t)} = {\sum\limits_{j = 1}^{M}\quad{{a\left( r_{j} \right)}{S_{j}\left( {t - \frac{r_{ij}}{c}} \right)}}}$ where i =1 to N.

Since the amplitudes of the sources X_(j) are unknown, the following equation can be written as follows, integrating the term a(r_(j)) in S_(j): ${s_{i}(t)} = {\sum\limits_{j = 1}^{M}{S_{j}\left( {t - \frac{r_{ij}}{c}} \right)}}$ where i=1 to N.

Using Fourier transforms, the expression for the signals s_(i)(t) becomes: $\begin{matrix} {{{\hat{s}}_{i}(\omega)} = {\sum\limits_{j = 1}^{M}{{\hat{\quad S}}_{j}{(\omega) \cdot {\mathbb{e}}^{{- J}\quad\omega\frac{r_{ij}}{c}}}}}} & (1) \end{matrix}$ where i=1 to N where ŝ and Ŝ are the Fourier transforms of s and S respectively and where ω is angular frequency.

This first equation (1) relates the received signals to the distance r_(ij), i.e. to the positions of the sources X_(j).

As can be seen in FIG. 2, other relationships can be expressed, associated with geometrical considerations enabling the distances r_(ij) to be related to the unit vector n_(j), which determines the direction defined by the center of gravity of the sensors and the source generating the signal S_(j). The position of the sensors is defined by the vector C_(i) constructed from the positions of the sensors Y_(i) and the position of their center of gravity. A development restricted to the first order of r_(ij) then provides: r _(ij) ≈r _(j) −<n _(j) , c _(i)>  (2) where i=1 to N and j=1 to M, and where <., .> is the scalar product.

Thus, by replacing r_(ij) by the approximate expression given in (2) and integrating the phase term: ${\mathbb{e}}^{{- J}\quad\omega\frac{r_{j}}{c}}$ which depends only on the source X_(j) in the magnitude Ŝ_(j)(ω), equation (1) can be written: $\begin{matrix} {{{\hat{s}}_{i}(\omega)} = {\sum\limits_{j = 1}^{M}\quad{{{\hat{S}}_{j}(\omega)} \cdot {\mathbb{e}}^{{- J}\quad\omega\frac{{< n_{j}},{c_{i} >}}{c}}}}} & (3) \end{matrix}$ where i=1 to N.

This relationship can also be expressed in matrix and vector form: $\begin{matrix} {{{\hat{s}}_{i}(\omega)} = {\sum\limits_{j = 1}^{M}\quad{{{\hat{S}}_{j}(\omega)} \cdot {T_{j}(\omega)}}}} & (4) \end{matrix}$ with, for ith coordinate of the vector T_(j): $\left( T_{j} \right)_{i} = {\mathbb{e}}^{{- J}\quad\omega\frac{{< n_{j}},{c_{i} >}}{c}}$ where i=1 to N. Or indeed: s(ω)=T·S(ω)   (5) where T=matrix having the general term: $T_{ij} = {\mathbb{e}}^{{- J}\quad\omega\frac{{< n_{j}},{c_{i} >}}{c}}$

When the sources X_(j) are not correlated, the signals S_(j) can be determined from the signals s_(i) of the vectors n_(j). Cross-correlation functions between S_(i) and S_(j) for i≠j are then minimized.

Once the minimization operation has been performed, after determining the directions n_(j), it is also possible to discover the magnitudes S_(j).

If N=M, i.e. if there are as many sensors as sources, then the system (5) can in general be inverted.

If N≧M, the problem can be reduced to a square system by premultiplying by: ^(t)T* i.e. by the conjugate transposed matrix of T· System (5) then becomes: ^(t) T*·s(ω)=^(t) T*·T·S(ω) I.e. S(ω)=(^(t) T*·T)⁻¹·^(t) T*·s(ω)   (6)

With the signals Ŝ expressed formally in this way, the correlation coefficients R_(ij) between the sources i and j are calculated formally by: $\begin{matrix} {{R_{ij} = \frac{\int_{- \infty}^{+ \infty}{{\Gamma_{ij}^{2}(\tau)}\quad{\mathbb{d}\tau}}}{{\Gamma_{ii}(0)} \cdot {\Gamma_{jj}(0)}}},{i \neq j}} & (7) \end{matrix}$ where Γ_(ij) can also be calculated formally from frequency magnitudes, giving: $\begin{matrix} {R_{ij} = \frac{\int_{- \infty}^{+ \infty}{{{{{\hat{S}}_{i}(\omega)}}^{2} \cdot {{{\hat{S}}_{i}(\omega)}}^{2}}{\mathbb{d}\omega}}}{\int_{- \infty}^{+ \infty}{{{{\hat{S}}_{i}(\omega)}}^{2}{{\mathbb{d}\omega} \cdot {\int_{- \infty}^{+ \infty}{{{{\hat{S}}_{j}(\omega)}}^{2}{\mathbb{d}\omega}}}}}}} & (8) \end{matrix}$

The function for minimizing is then: $\begin{matrix} {{f\left( {n_{1},\ldots\quad,n_{j},\ldots\quad,n_{N}} \right)} = {\sum\limits_{k \neq 1}\quad R_{k1}}} & (9) \end{matrix}$ where the coefficients R_(kl) are functions of the vectors n_(j).

When the signals S_(i), S_(j) are received with comparable amplitudes, the denominators of R_(ij) are of the same order of magnitude and can then be replaced by 1 without spoiling the positions of the minimas. Calculating the Γ_(ij) can then advantageously be performed in the time domain, when the range of variation in possible delays is small.

Once the directions defined by the vectors n_(j) have been determined, it is also possible to find the magnitudes S_(j) from equation (6). Such a technique thus makes it possible to determine the natures of the sources X_(j).

The description below with reference to FIG. 3 gives an example of detecting and locating two noise sources X₁, X₂ that are not correlated (M=2), using two sensors Y₁, Y₂ (N=2).

In the frequency domain, the electrical signals s₁, s₂ delivered respectively by the sensors Y₁ and Y₂ and representative of the sum of the signals S₁, S₂ emitted by the noise sources X₁, X₂ are expressed as follows: $\left\{ \begin{matrix} {{{\hat{s}}_{1}(\omega)} = {{{\mathbb{e}}^{{- J}\quad{\omega\tau}_{11}}{{\hat{S}}_{1}(\omega)}} + {{\mathbb{e}}^{{- J}\quad{\omega\tau}_{21}}{{\hat{S}}_{2}(\omega)}}}} \\ {{{\hat{s}}_{2}(\omega)} = {{{\mathbb{e}}^{{- J}\quad{\omega\tau}_{12}}{{\hat{S}}_{1}(\omega)}} + {{\mathbb{e}}^{{- J}\quad{\omega\tau}_{22}}{{\hat{S}}_{2}(\omega)}}}} \end{matrix} \right.$ where $\tau_{ij} = \frac{r_{ij}}{c}$ is the propagation delay of the signal emitted by source i prior to reaching sensor j.

Inverting this system leads to: $\left\{ \begin{matrix} {{{\hat{S}}_{1}(\omega)} = \frac{{{{\hat{s}}_{1}(\omega)}{\mathbb{e}}^{{- J}\quad{\omega\tau}_{22}}} - {{{\hat{s}}_{2}(\omega)}{\mathbb{e}}^{{- J}\quad{\omega\tau}_{21}}}}{{\mathbb{e}}^{{- J}\quad{\omega{({\tau_{11} + \tau_{22}})}}} - {\mathbb{e}}^{{- J}\quad{\omega{({\tau_{12} + \tau_{21}})}}}}} \\ {{{\hat{S}}_{2}(\omega)} = \frac{{{{\hat{s}}_{2}(\omega)}{\mathbb{e}}^{{- J}\quad{\omega\tau}_{11}}} - {{{\hat{s}}_{1}(\omega)}{\mathbb{e}}^{{- J}\quad{\omega\tau}_{12}}}}{{\mathbb{e}}^{{- J}\quad{\omega{({\tau_{11} + \tau_{22}})}}} - {\mathbb{e}}^{{- J}\quad{\omega{({\tau_{12} + \tau_{21}})}}}}} \end{matrix} \right.$

The cross-correlation function between the source signals S₁ and S₂ is written: Γ₁₂(τ) = ∫_(−∞)^(+∞)Ŝ₁(ω) ⋅ Ŝ₂(ω)𝕖^(J  ωτ)  𝕕ω for the delay τ.

Replacing Ŝ₁(ω) and Ŝ₂(ω), it becomes: ${\Gamma_{12}(\tau)} = {\int_{- \infty}^{+ \infty}{\frac{N(\omega)}{{{D(\omega)}}^{2}}{\mathbb{d}\omega}}}$ whence ${N(\omega)} = {\begin{bmatrix} {{{- {{{\hat{s}}_{1}(\omega)}}^{2}}{\mathbb{e}}^{J\quad{\omega{({\tau_{12} - \tau_{22}})}}}} - {{{{\hat{s}}_{2}(\omega)}}^{2}{\mathbb{e}}^{J\quad{\omega{({\tau_{11} - \tau_{21}})}}}} +} \\ {{{{\hat{s}}_{1}(\omega)}{{\hat{s}}_{2}^{*}(\omega)}{\mathbb{e}}^{J\quad{\omega{({\tau_{11} - \tau_{22}})}}}} + {{{\hat{s}}_{1}^{*}(\omega)}{{\hat{s}}_{2}(\omega)}{\mathbb{e}}^{J\quad{\omega{({\tau_{12} - \tau_{21}})}}}}} \end{bmatrix} \cdot {\mathbb{e}}^{J\quad{\omega\tau}}}$ and ${{D(\omega)}}^{2} = {4\sin^{2}\frac{\omega}{2}\left( {\tau_{11} + \tau_{22} - \tau_{12} - \tau_{21}} \right)}$

A sample (but sub-optimal) solution in this case consists in optimizing the numerator N only.

The cross-correlation Γ₁₂ can then be approximated by: Γ₁₂(τ) = ∫_(−∞)^(+∞)N(ω)  𝕕ω

Replacing N(ω) by its value an expression is obtained which is a function only of the γ_(ij) corresponding to the autocorrelations and cross-correlations between the measured signals s_(i) and s_(j): Γ₁₂(τ)≅−γ₁₁(τ+τ₁₂−τ₂₂)−γ₂₂(τ+τ₁₁−τ₂₁ )+γ₁₂(τ+τ₁₁−τ₂₂)+γ₂₁(τ+τ₁₂−τ₂₁)

It is recalled that the distance r_(ij) can be approximated by: r _(ij) ≈r _(j) −<n _(j) , c _(i)>

Thus, replacing r_(ij) in this approximate expression and integrating the phase term ${\mathbb{e}}^{{- J}\quad\omega\frac{r_{j}}{c}}$ in S_(j)(ω) finally leads to an expression of the estimator of Γ₁₂ which is as follows: $\begin{matrix} {{\Gamma_{12}(\tau)} \approx {{- {\gamma_{11}\left( {\tau - \frac{{< n_{2}},{c_{1} >}}{c} + \frac{{< n_{2}},{c_{2} >}}{c}} \right)}} -}} \\ {{\gamma_{22}\left( {\tau - \frac{{< n_{1}},{c_{1} >}}{c} + \frac{{< n_{1}},{c_{2} >}}{c}} \right)} +} \\ {{\gamma_{12}\left( {\tau - \frac{{< n_{1}},{c_{1} >}}{c} + \frac{{< n_{2}},{c_{2} >}}{c}} \right)} + {\gamma_{21}\left( {\tau - \frac{{< n_{2}},{c_{1} >}}{c} + \frac{{< n_{1}},{c_{2} >}}{c}} \right)}} \end{matrix}$ where n_(j)=the unit vector of (OX_(i)) with i=1, 2. However: ${< n_{1}},{c_{1}>={{- \frac{D}{2}}\quad\cos\quad\theta_{1}} < n_{1}},{c_{2}>={\frac{D}{2}\quad\cos\quad\theta_{1}} < n_{2}},{c_{1}>={{- \frac{D}{2}}\quad\cos\quad\theta_{2}} < n_{2}},{c_{2}>={{- \frac{D}{2}}\quad\cos\quad\theta_{2}}}$ Where the distance between sensors is written is D. Then: ${\Gamma_{12}(\tau)} \approx {{- {\gamma_{11}\left( {\tau + {\frac{D}{c}\cos\quad\theta_{1}}} \right)}}\quad - {\gamma_{22}\left( {\tau + {\frac{D}{2}\quad\cos\quad\theta_{1}}} \right)} + \quad{\gamma_{12}\left( {\tau + {\frac{D}{2c}\quad\left( {{\cos\quad\theta_{1}} + {\cos\quad\theta_{2}}} \right)}} \right)} + \quad{\gamma_{21}\left( {\tau + {\frac{D}{2c}\left( \quad{{\cos\quad\theta_{1}}\quad + {\cos\quad\theta_{2}}} \right)}} \right)}}$

The functional to be minimized relative to (θ₁, θ₂) is thus: R₁₂ = ∫_(−∞)^(+∞)Γ₁₂²(τ)  𝕕τ

Sign ambiguity between θ₁ and θ₂ is removed by analyzing the half-plane containing the sources and assumed to be known a priori.

The invention is not limited to the examples described and shown, since various modifications can be made thereto without going beyond this ambit.

Without further elaboration, it is believed that one skilled in the art can, using the preceding description, utilize the present invention to its fullest extent. The preceding preferred specific embodiments are, therefore, to be construed as merely illustrative, and not limitative of the remainder of the disclosure in any way whatsoever. Also, any preceding examples can be repeated with similar success by substituting the generically or specifically described reactants and/or operating conditions of this invention for those used in such examples.

Throughout the specification and claims, all temperatures are set forth uncorrected in degrees Celsius and, all parts and percentages are by weight, unless otherwise indicated.

The entire disclosure of all applications, patents and publications, cited herein are incorporated by reference herein.

From the foregoing description, one skilled in the art can easily ascertain the essential characteristics of this invention and, without departing from the spirit and scope thereof, can make various changes and modifications of the invention to adapt it to various usages and conditions. 

1. A method of detecting and locating noise sources each emitting respective signals S_(j) where j=1 to M, detection being provided by means of acoustic wave or vibration sensors each delivering a respective time-varying electrical signal s_(i) with i varying from 1 to N, the method consisting: in taking the time-varying electrical signals delivered by the sensors, each signal s_(i)(t) delivered by a sensor being the sum of the signals S_(j) emitted by the noise sources; in amplifying and filtering the taken time-varying electrical signals; in digitizing the electrical signals; in calculating the functional ${f\left( {n_{1},\ldots\quad,n_{j},\ldots\quad,n_{N}} \right)} = {\sum\limits_{k \neq 1}^{\quad}\quad R_{k1}}$ with the coefficients R_(kl) being a function of the vectors n_(j) giving the directions of the noise sources; and in minimizing the functional f in such a manner as to determine the directions n_(j) of the noise sources.
 2. A method according to claim 1, wherein, in order to minimize the functional f, the method consists in: calculating the Fourier transforms of the signals s_(i)(t) delivered by the sensors; formally calculating the coefficients R_(ij): $R_{ij} = \frac{\int_{- \infty}^{+ \infty}{{{{{\hat{S}}_{i}(\omega)}}^{2} \cdot {{{\hat{S}}_{i}(\omega)}}^{2}}\quad{\mathbb{d}\omega}}}{\int_{- \infty}^{+ \infty}{{{{\hat{S}}_{i}(\omega)}}^{2}\quad{{\mathbb{d}\omega} \cdot {\int_{- \infty}^{+ \infty}{{{{\hat{S}}_{j}(\omega)}}^{2}{\mathbb{d}\omega}}}}}}$ and minimizing the functional f in order to determine the directions n_(j) of the selected noise sources.
 3. A detection method according to claim 1, wherein, in order to minimize the functional f, the method consists: in formally calculating the correlation coefficient R_(ij): $R_{ij} = \frac{\int_{- \infty}^{+ \infty}{{\Gamma_{ij}^{2}(\tau)}\quad{\mathbb{d}\tau}}}{{\Gamma_{ii}(0)} \cdot {\Gamma_{jj}(0)}}$ where Γ_(ij) is the cross-correlation function between the signals S_(i) and S_(j).
 4. A detection method according to claim 1, wherein, after performing the minimization operation, the method consists in calculating the source vector: S(w)=(^(t) T*·T)⁻¹·^(t) T*·s(ω) in order to find the characteristics of the noise sources. 